The number of text messages (t) that katie sends depends on the number of days (d) she is on vacation. the equation is t=50d+20.

1 answer:

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Based on the equation katie gets 20 text messages + 50 more for each day she is away.
therefore the number 50 shows how much the number of text messages (t) increases for each day she is away.

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Arlecino [84]

I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set $y=1.25$ for this example.)

The length of each cross section (the side lying in the base) has length determined by the horizontal distance $x$ between the y-axis $x=0$ and the curve $y=\sqrt x$ . In terms of $y$ , this distance is $x=y^2$ . The height of each cross section is twice the value of $y$ , so the area of each rectangular cross section should be $2y^3$ .

This means the volume would be given by the integral

$\displaystyle\int_0^22y^3\,\mathrm dy$